schktp.f

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*> \brief \b SCHKTP
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
*                          NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
*                          IWORK, NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NMAX, NN, NNS, NOUT
*       REAL               THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
*       REAL               AINVP( * ), AP( * ), B( * ), RWORK( * ),
*      $                   WORK( * ), X( * ), XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SCHKTP tests STPTRI, -TRS, -RFS, and -CON, and SLATPS
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] DOTYPE
*> \verbatim
*>          DOTYPE is LOGICAL array, dimension (NTYPES)
*>          The matrix types to be used for testing.  Matrices of type j
*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*>          NN is INTEGER
*>          The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*>          NVAL is INTEGER array, dimension (NN)
*>          The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*>          NNS is INTEGER
*>          The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*>          NSVAL is INTEGER array, dimension (NNS)
*>          The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is REAL
*>          The threshold value for the test ratios.  A result is
*>          included in the output file if RESULT >= THRESH.  To have
*>          every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*>          TSTERR is LOGICAL
*>          Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[in] NMAX
*> \verbatim
*>          NMAX is INTEGER
*>          The leading dimension of the work arrays.  NMAX >= the
*>          maximumm value of N in NVAL.
*> \endverbatim
*>
*> \param[out] AP
*> \verbatim
*>          AP is REAL array, dimension
*>                      (NMAX*(NMAX+1)/2)
*> \endverbatim
*>
*> \param[out] AINVP
*> \verbatim
*>          AINVP is REAL array, dimension
*>                      (NMAX*(NMAX+1)/2)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is REAL array, dimension (NMAX*NSMAX)
*>          where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension
*>                      (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (NMAX)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension
*>                      (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>          The unit number for output.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE schktp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
     $                   NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
     $                   IWORK, NOUT )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      LOGICAL            TSTERR
      INTEGER            NMAX, NN, NNS, NOUT
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
      REAL               AINVP( * ), AP( * ), B( * ), RWORK( * ),
     $                   work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NTYPE1, NTYPES
      PARAMETER          ( NTYPE1 = 10, ntypes = 18 )
      INTEGER            NTESTS
      parameter( ntests = 9 )
      INTEGER            NTRAN
      parameter( ntran = 3 )
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      CHARACTER          DIAG, NORM, TRANS, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, IDIAG, IMAT, IN, INFO, IRHS, ITRAN, IUPLO,
     $                   k, lap, lda, n, nerrs, nfail, nrhs, nrun
      REAL               AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
     $                   SCALE
*     ..
*     .. Local Arrays ..
      CHARACTER          TRANSS( NTRAN ), UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      REAL               RESULT( NTESTS )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLANTP
      EXTERNAL           lsame, slantp
*     ..
*     .. External Subroutines ..
      EXTERNAL           alaerh, alahd, alasum, scopy, serrtr, sget04,
     $                   slacpy, slarhs, slatps, slattp, stpcon, stprfs,
     $                   stpt01, stpt02, stpt03, stpt05, stpt06, stptri,
     $                   stptrs
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, IOUNIT
*     ..
*     .. Common blocks ..
      COMMON             / infoc / infot, iounit, ok, lerr
      COMMON             / srnamc / srnamt
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Data statements ..
      DATA               iseedy / 1988, 1989, 1990, 1991 /
      DATA               uplos / 'U', 'L' / , transs / 'N', 'T', 'C' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      path( 1: 1 ) = 'Single precision'
      path( 2: 3 ) = 'TP'
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
*     Test the error exits
*
      IF( tsterr )
     $   CALL serrtr( path, nout )
      infot = 0
*
      DO 110 in = 1, nn
*
*        Do for each value of N in NVAL
*
         n = nval( in )
         lda = max( 1, n )
         lap = lda*( lda+1 ) / 2
         xtype = 'N'
*
         DO 70 imat = 1, ntype1
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
            IF( .NOT.dotype( imat ) )
     $         GO TO 70
*
            DO 60 iuplo = 1, 2
*
*              Do first for UPLO = 'U', then for UPLO = 'L'
*
               uplo = uplos( iuplo )
*
*              Call SLATTP to generate a triangular test matrix.
*
               srnamt = 'SLATTP'
               CALL slattp( imat, uplo, 'no transpose', DIAG, ISEED, N,
     $                      AP, X, WORK, INFO )
*
*              Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
               IF( LSAME( DIAG, 'n' ) ) THEN
                  IDIAG = 1
               ELSE
                  IDIAG = 2
               END IF
*
*+    TEST 1
*              Form the inverse of A.
*
.GT.               IF( N0 )
     $            CALL SCOPY( LAP, AP, 1, AINVP, 1 )
               SRNAMT = 'stptri'
               CALL STPTRI( UPLO, DIAG, N, AINVP, INFO )
*
*              Check error code from STPTRI.
*
.NE.               IF( INFO0 )
     $            CALL ALAERH( PATH, 'stptri', INFO, 0, UPLO // DIAG, N,
     $                         N, -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
*              Compute the infinity-norm condition number of A.
*
               ANORM = SLANTP( 'i', uplo, diag, n, ap, rwork )
               ainvnm = slantp( 'I', uplo, diag, n, ainvp, rwork )
               IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
                  rcondi = one
               ELSE
                  rcondi = ( one / anorm ) / ainvnm
               END IF
*
*              Compute the residual for the triangular matrix times its
*              inverse.  Also compute the 1-norm condition number of A.
*
               CALL stpt01( uplo, diag, n, ap, ainvp, rcondo, rwork,
     $                      result( 1 ) )
*
*              Print the test ratio if it is .GE. THRESH.
*
               IF( result( 1 ).GE.thresh ) THEN
                  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $               CALL alahd( nout, path )
                  WRITE( nout, fmt = 9999 )uplo, diag, n, imat, 1,
     $               result( 1 )
                  nfail = nfail + 1
               END IF
               nrun = nrun + 1
*
               DO 40 irhs = 1, nns
                  nrhs = nsval( irhs )
                  xtype = 'N'
*
                  DO 30 itran = 1, ntran
*
*                 Do for op(A) = A, A**T, or A**H.
*
                     trans = transs( itran )
                     IF( itran.EQ.1 ) THEN
                        norm = 'O'
                        rcondc = rcondo
                     ELSE
                        norm = 'I'
                        rcondc = rcondi
                     END IF
*
*+    TEST 2
*                 Solve and compute residual for op(A)*x = b.
*
                     srnamt = 'SLARHS'
                     CALL slarhs( path, xtype, uplo, trans, n, n, 0,
     $                            idiag, nrhs, ap, lap, xact, lda, b,
     $                            lda, iseed, info )
                     xtype = 'C'
                     CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
*
                     srnamt = 'stptrs'
                     CALL STPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, X,
     $                            LDA, INFO )
*
*                 Check error code from STPTRS.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'stptrs', INFO, 0,
     $                               UPLO // TRANS // DIAG, N, N, -1,
     $                               -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
                     CALL STPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X,
     $                            LDA, B, LDA, WORK, RESULT( 2 ) )
*
*+    TEST 3
*                 Check solution from generated exact solution.
*
                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                            RESULT( 3 ) )
*
*+    TESTS 4, 5, and 6
*                 Use iterative refinement to improve the solution and
*                 compute error bounds.
*
                     SRNAMT = 'stprfs'
                     CALL STPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B,
     $                            LDA, X, LDA, RWORK, RWORK( NRHS+1 ),
     $                            WORK, IWORK, INFO )
*
*                 Check error code from STPRFS.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'stprfs', INFO, 0,
     $                               UPLO // TRANS // DIAG, N, N, -1,
     $                               -1, NRHS, IMAT, NFAIL, NERRS,
     $                               NOUT )
*
                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                            RESULT( 4 ) )
                     CALL STPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B,
     $                            LDA, X, LDA, XACT, LDA, RWORK,
     $                            RWORK( NRHS+1 ), RESULT( 5 ) )
*
*                    Print information about the tests that did not pass
*                    the threshold.
*
                     DO 20 K = 2, 6
.GE.                        IF( RESULT( K )THRESH ) THEN
.EQ..AND..EQ.                           IF( NFAIL0  NERRS0 )
     $                        CALL ALAHD( NOUT, PATH )
                           WRITE( NOUT, FMT = 9998 )UPLO, TRANS, DIAG,
     $                        N, NRHS, IMAT, K, RESULT( K )
                           NFAIL = NFAIL + 1
                        END IF
   20                CONTINUE
                     NRUN = NRUN + 5
   30             CONTINUE
   40          CONTINUE
*
*+    TEST 7
*                 Get an estimate of RCOND = 1/CNDNUM.
*
               DO 50 ITRAN = 1, 2
.EQ.                  IF( ITRAN1 ) THEN
                     NORM = 'o'
                     RCONDC = RCONDO
                  ELSE
                     NORM = 'i'
                     RCONDC = RCONDI
                  END IF
*
                  SRNAMT = 'stpcon'
                  CALL STPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK,
     $                         IWORK, INFO )
*
*                 Check error code from STPCON.
*
.NE.                  IF( INFO0 )
     $               CALL ALAERH( PATH, 'stpcon', INFO, 0,
     $                            NORM // UPLO // DIAG, N, N, -1, -1,
     $                            -1, IMAT, NFAIL, NERRS, NOUT )
*
                  CALL STPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK,
     $                         RESULT( 7 ) )
*
*                 Print the test ratio if it is .GE. THRESH.
*
.GE.                  IF( RESULT( 7 )THRESH ) THEN
.EQ..AND..EQ.                     IF( NFAIL0  NERRS0 )
     $                  CALL ALAHD( NOUT, PATH )
                     WRITE( NOUT, FMT = 9997 ) 'stpcon', NORM, UPLO,
     $                  DIAG, N, IMAT, 7, RESULT( 7 )
                     NFAIL = NFAIL + 1
                  END IF
                  NRUN = NRUN + 1
   50          CONTINUE
   60       CONTINUE
   70    CONTINUE
*
*        Use pathological test matrices to test SLATPS.
*
         DO 100 IMAT = NTYPE1 + 1, NTYPES
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
.NOT.            IF( DOTYPE( IMAT ) )
     $         GO TO 100
*
            DO 90 IUPLO = 1, 2
*
*              Do first for UPLO = 'U', then for UPLO = 'L'
*
               UPLO = UPLOS( IUPLO )
               DO 80 ITRAN = 1, NTRAN
*
*                 Do for op(A) = A, A**T, or A**H.
*
                  TRANS = TRANSS( ITRAN )
*
*                 Call SLATTP to generate a triangular test matrix.
*
                  SRNAMT = 'slattp'
                  CALL SLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, X,
     $                         WORK, INFO )
*
*+    TEST 8
*                 Solve the system op(A)*x = b.
*
                  SRNAMT = 'slatps'
                  CALL SCOPY( N, X, 1, B, 1 )
                  CALL SLATPS( UPLO, TRANS, DIAG, 'n', n, ap, b, scale,
     $                         rwork, info )
*
*                 Check error code from SLATPS.
*
                  IF( info.NE.0 )
     $               CALL alaerh( path, 'SLATPS', info, 0,
     $                            uplo // trans // diag // 'N', n, n,
     $                            -1, -1, -1, imat, nfail, nerrs, nout )
*
                  CALL stpt03( uplo, trans, diag, n, 1, ap, scale,
     $                         rwork, one, b, lda, x, lda, work,
     $                         result( 8 ) )
*
*+    TEST 9
*                 Solve op(A)*x = b again with NORMIN = 'Y'.
*
                  CALL scopy( n, x, 1, b( n+1 ), 1 )
                  CALL slatps( uplo, trans, diag, 'Y', n, ap, b( n+1 ),
     $                         scale, rwork, info )
*
*                 Check error code from SLATPS.
*
                  IF( info.NE.0 )
     $               CALL alaerh( path, 'SLATPS', info, 0,
     $                            uplo // trans // diag // 'Y', n, n,
     $                            -1, -1, -1, imat, nfail, nerrs, nout )
*
                  CALL stpt03( uplo, trans, diag, n, 1, ap, scale,
     $                         rwork, one, b( n+1 ), lda, x, lda, work,
     $                         result( 9 ) )
*
*                 Print information about the tests that did not pass
*                 the threshold.
*
                  IF( result( 8 ).GE.thresh ) THEN
                     IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                  CALL alahd( nout, path )
                     WRITE( nout, fmt = 9996 )'SLATPS', uplo, trans,
     $                  diag, 'N', n, imat, 8, result( 8 )
                     nfail = nfail + 1
                  END IF
                  IF( result( 9 ).GE.thresh ) THEN
                     IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                  CALL alahd( nout, path )
                     WRITE( nout, fmt = 9996 )'SLATPS', uplo, trans,
     $                  diag, 'Y', n, imat, 9, result( 9 )
                     nfail = nfail + 1
                  END IF
                  nrun = nrun + 2
   80          CONTINUE
   90       CONTINUE
  100    CONTINUE
  110 CONTINUE
*
*     Print a summary of the results.
*
      CALL alasum( path, nout, nfail, nrun, nerrs )
*
 9999 FORMAT( ' UPLO=''', a1, ''', DIAG=''', a1, ''', N=', i5,
     $      ', type ', i2, ', test(', i2, ')= ', g12.5 )
 9998 FORMAT( ' UPLO=''', a1, ''', TRANS=''', a1, ''', DIAG=''', a1,
     $      ''', N=', i5, ''', NRHS=', i5, ', type ', i2, ', test(',
     $      i2, ')= ', g12.5 )
 9997 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ''', a1, ''',',
     $      i5, ', ... ), type ', i2, ', test(', i2, ')=', g12.5 )
 9996 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ''', a1, ''', ''',
     $      a1, ''',', i5, ', ... ), type ', i2, ', test(', i2, ')=',
     $      g12.5 )
      RETURN
*
*     End of SCHKTP
*
      END